SOLUTION: Perform the indicated operations and reduce to lowest terms 2/x-3+3/3-x

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Question 164947This question is from textbook
: Perform the indicated operations and reduce to lowest terms
2/x-3+3/3-x
This question is from textbook

Answer by MRperkins(300) About Me  (Show Source):
You can put this solution on YOUR website!
I am guessing that you have left out some parenthesis(). If in doubt put parenthesis around nearly everything. I think the problem is supposed to be 2/(x-3)+3/(3-x) which looks like this: 2%2F%28x-3%29%2B3%2F%283-x%29
However the problem that you wrote would have looked like this: 2%2Fx-3%2B3%2F3-x
With that said...
in order to add two numbers they must have the same denominator. If we look at the denominators:x-3 and 3-x we notice that one of them is the exact opposite of the other or the negative. So factor out a -1 from 3-x and you get -1(-3+x) which can be written -1(x-3)
.
So now we have 2%2F%28x-3%29%2B3%2F%28-1%28x-3%29%29
.
Multiply the top and bottom of: 3%2F%28-1%28x-3%29%29 by -1
and you get: -3%2F%28x-3%29
Now the whole formula can be written 2%2F%28x-3%29-3%2F%28x-3%29
.
Since the denominators are the same now we can add the two expressions.
%282-3%29%2F%28x-3%29
or -1%2F%28x-3%29
.
.
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